ABSTRACT
Cauchy-Born Rule ....................................................................... 129 Keywords .............................................................................................. 149
4.1 INTRODUCTION
CNTs are at the boundary between small structures and large molecules. Reflecting their condition, single-scale modeling approaches can be generally classified into two categories: atomistic and continuous modeling. For the former approach, the methods are very general [218] but their operable application is limited to small and short-lived systems because they are computationally expensive. In the past, interactions were obtained by twobody potentials with simple analytical form (Morse and Lennard-Jones). Recently, many-body terms are accounted in the most accurate potentials, as described in the following sections. As a result, their complexity is usually polynomial but seldom linear on the number of atoms [219]. The latter approach simplifies the model by treating CNTs as continuous elastic shells, extending the already large and fruitful knowledge from CM. However, many of these models seems to be far too reductionist. To some extent, their basic approaches neglect the detailed characteristics of chirality and are almost unable to account for forces acting on individual atoms (and their eventual vacancies that constitute realistic defects). Many authors have analyzed the mechanics of carbon nanotubes through CM, but the relevance of continuous models for systems composed by few atoms is controversial [40, 48, 220-222].
